Finite Group Databasebeta

← Group #11923238

Character table — Group #11923238

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order1222344666233466666666121212122244443366666612121212224441212666666121212121212121212122266666121212121212444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-11111111111111-1-111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ411111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111+i321+i321−i321−i32111+i321+i321−i321−i32-1-1-11+i321−i321+i321−i32
χ511111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ611111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111−i321−i321+i321+i32111−i321−i321+i321+i32-1-1-11−i321+i321−i321+i32
χ71111111111-111-1-1-1111111-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111111-1-11111-11-1-1-1-1-1
χ81111111111-111-1-1-1111111-1-111-1-111-1-1111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-111111
χ91111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-1-1111+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32111−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32-11-11+i321−i321+i321−i32
χ101111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111-1-1111+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-111+i321+i321−i321−i32-1-11+i321+i321−i321−i321-11−1−i32−1+i32−1−i32−1+i32
χ111111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-1-1111−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32111−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32-11-11−i321+i321−i321+i32
χ121111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111-1-1111−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-111−i321−i321+i321+i32-1-11−i321−i321+i321+i321-11−1+i32−1−i32−1+i32−1−i32
χ1311111-1-1111111-111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1-111
χ1411111-1-1111111-111111111-1-1-1-1-1-1111111111111-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-1111-1-1
χ1511111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1−1−i32−1−i32−1+i32−1+i32-111+i321+i321−i321−i3211-11+i321−i32−1−i32−1+i32
χ1611111-1-11111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-11+i321+i321−i321−i32-11−1−i32−1−i32−1+i32−1+i32-1-11−1−i32−1+i321+i321−i32
χ1711111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1−1+i32−1+i32−1−i32−1−i32-111−i321−i321+i321+i3211-11−i321+i32−1+i32−1−i32
χ1811111-1-11111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-11−i321−i321+i321+i32-11−1+i32−1+i32−1−i32−1−i32-1-11−1+i32−1−i321−i321+i32
χ1911111-1-1111-1111-1-111111111-1-11111-1-111111111-1-1-1-1-11-11-111-1-1-1-1-1-111-1-111-1-111-1-1-111111-1-1-1-1-1-11111-1-1
χ2011111-1-1111-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-111-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-11-111111-1-1-1-111
χ2111111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-11-1111+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1-1−1−i32−1−i32−1+i32−1+i321-11+i321+i321−i321−i32-111−1−i32−1+i321+i321−i32
χ2211111-1-1111-1−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111-1111+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-11+i321+i321−i321−i321-1−1−i32−1−i32−1+i32−1+i321-1-11+i321−i32−1−i32−1+i32
χ2311111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-11-1111−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1-1−1+i32−1+i32−1−i32−1−i321-11−i321−i321+i321+i32-111−1+i32−1−i321−i321+i32
χ2411111-1-1111-1−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111-1111−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-11−i321−i321+i321+i321-1−1+i32−1+i32−1−i32−1−i321-1-11−i321+i32−1+i32−1−i32
χ252222-122-1-1-12222-1-1222222-1-1-1-1002200-1-1-1-1-1-1-1-1222220022-1-122-1-1-1-122-1-1-1-1-1-1-1-100-10000-1-100000000000
χ262222-122-1-1-12−1−i3−1+i32-1-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-10022001+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i320022-1-1−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i3200-10000-1-100000000000
χ272222-122-1-1-12−1+i3−1−i32-1-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-1-10022001−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i320022-1-1−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i3200-10000-1-100000000000
χ282222-122-1-1-1-222-21122222211-1-1002200-1-1-1-1-1-1-1-12222200-2-2-1-1-2-21111-2-2-1-111-1-11100-100001100000000000
χ292222-122-1-1-1-2−1−i3−1+i3-211−1−i3−1+i3−1−i3−1−i3−1+i3−1+i311-1-10022001+i321−i321+i321−i321+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i3200-2-2-1-11+i31−i3−1−i32−1−i32−1+i32−1+i321+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200-100001100000000000
χ302222-122-1-1-1-2−1+i3−1−i3-211−1+i3−1−i3−1+i3−1+i3−1−i3−1−i311-1-10022001−i321+i321−i321+i321−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i3200-2-2-1-11−i31+i3−1+i32−1+i32−1−i32−1−i321−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200-100001100000000000
χ312222-1-2-2-1-1-1222-2-1-12222221111002200-1-1-1-1-1-1-1-1-2-2-2-2-200-22-1-122-1-1-1-1-2-21111111100100001-100000000000
χ322222-1-2-2-1-1-12−1−i3−1+i3-2-1-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i311110022001+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i3-200-22-1-1−1−i3−1+i31+i321+i321−i321−i321+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200100001-100000000000
χ332222-1-2-2-1-1-12−1+i3−1−i3-2-1-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i311110022001−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i3-200-22-1-1−1+i3−1−i31−i321−i321+i321+i321−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200100001-100000000000
χ342222-1-2-2-1-1-1-222211222222-1-111002200-1-1-1-1-1-1-1-1-2-2-2-2-2002-2-1-1-2-211112211-1-111-1-10010000-1100000000000
χ352222-1-2-2-1-1-1-2−1−i3−1+i3211−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1110022001+i321−i321+i321−i321+i321+i321−i321−i321+i31+i31−i31−i3-2002-2-1-11+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i320010000-1100000000000
χ362222-1-2-2-1-1-1-2−1+i3−1−i3211−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1110022001−i321+i321−i321+i321−i321−i321+i321+i321−i31−i31+i31+i3-2002-2-1-11−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i320010000-1100000000000
χ372-2-22200-2-22022000-2-22-22-20000002-22-222-2-22-22-20000000002-200000000000000002-200000002-22-20000000
χ382-2-22200-2-22022000-2-22-22-20000002-2-2222-2-22-22-20000000002-20000000000000000-220000000-22-220000000
χ392-2-22200-2-220−1−i3−1+i30001+i31−i3−1−i31+i3−1+i31−i30000002-22-2−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000000002-200000000000000002-20000000−1−i31+i3−1+i31−i30000000
χ402-2-22200-2-220−1−i3−1+i30001+i31−i3−1−i31+i3−1+i31−i30000002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000000002-20000000000000000-2200000001+i3−1−i31−i3−1+i30000000
χ412-2-22200-2-220−1+i3−1−i30001−i31+i3−1+i31−i3−1−i31+i30000002-22-2−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000000002-200000000000000002-20000000−1+i31−i3−1−i31+i30000000
χ422-2-22200-2-220−1+i3−1−i30001−i31+i3−1+i31−i3−1−i31+i30000002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000000002-20000000000000000-2200000001−i3−1+i31+i3−1−i30000000
χ433333333333300333000000333333-1-133000000000000-133-1-1-1-10000000000000000-1-1-10000-1-10000-1-1-10000
χ4433333333333003330000003333-3-3-1-1-3-3000000000000-1-3-3-1-1-1-1000000000000000011-10000-1-100001110000
χ453333333333-300-3-3-3000000-3-33333-1-133000000000000-1-3-311-1-10000000000000000-1-1-100001100001-110000
χ463333333333-300-3-3-3000000-3-333-3-3-1-1-3-3000000000000-13311-1-1000000000000000011-10000110000-11-10000
χ4733333-3-3333300-333000000-3-3-3-333-1-1-3-30000000000001-331-1-1-1000000000000000011100001-10000-1-110000
χ4833333-3-3333300-333000000-3-3-3-3-3-3-1-13300000000000013-31-1-1-10000000000000000-1-1100001-1000011-10000
χ4933333-3-3333-3003-3-300000033-3-333-1-1-3-300000000000013-3-11-1-100000000000000001110000-1100001-1-10000
χ5033333-3-3333-3003-3-300000033-3-3-3-3-1-1330000000000001-33-11-1-10000000000000000-1-110000-110000-1110000
χ5144-4-44004-4-40-2-2000222-22-200004-40000-2-2222-22-20000000000000000000000000000002-22-20000000000000
χ5244-4-44004-4-40-2-2000222-22-20000-440000-2-2222-22-2000000000000000000000000000000-22-220000000000000
χ5344-4-44004-4-401+i31−i3000−1−i3−1+i3−1−i31+i3−1+i31−i300004-400001+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000−1−i31+i3−1+i31−i30000000000000
χ5444-4-44004-4-401+i31−i3000−1−i3−1+i3−1−i31+i3−1+i31−i30000-4400001+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000001+i3−1−i31−i3−1+i30000000000000
χ5544-4-44004-4-401−i31+i3000−1+i3−1−i3−1+i31−i3−1−i31+i300004-400001−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000−1+i31−i3−1−i31+i30000000000000
χ5644-4-44004-4-401−i31+i3000−1+i3−1−i3−1+i31−i3−1−i31+i30000-4400001−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000000001−i3−1+i31+i3−1−i30000000000000
χ574-44-444i−4i-44-40-2-2000-2-22222004i−4i000000-2-2-2-222222i−2i2i−2i0000000000000002i−2i002i−2i0000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.